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A296009 Smallest number m such that (2n-1)*m has only odd digits. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 5, 3, 5, 11, 1, 1, 1, 1, 1, 13, 13, 3, 11, 11, 1, 1, 1, 1, 1, 13, 5, 3, 5, 11, 1, 1, 1, 1, 1, 17, 11, 7, 11, 11, 1, 1, 1, 1, 1, 11, 5, 3, 5, 11, 1, 1, 1, 1, 1, 11, 11, 3, 11, 15, 1, 1, 1, 1, 1, 11, 5, 11, 5, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

Record values:

1 * 1 = 1

21 * 15 = 315

81 * 17 = 1377

167 * 19 = 3173

169 * 33 = 5577

201 * 155 = 31155

633 * 283 = 179139

1011 * 743 = 751173

1101 * 833 = 917133

2001 * 1555 = 3111555

9091 * 4309 = 39173119

9901 * 32231 = 319119131

91001 * 34193 = 3111597193

100011 * 37927 = 3793117197

101001 * 58553 = 5913911553

200001 * 155555 = 31111155555

909091 * 431109 = 391917311919

990001 * 12121113 = 11999913991113

999001 * 31222311 = 31191119911311

... (above are exhaustive)

99990001 * 31122223111 = 3111911119991113111 (verified smallest)

9999900001 * 31112222231111 = 311119111119999111131111 (not verified smallest)

LINKS

Yang Haoran, Table of n, a(n) for n = 1..10001

Yang Haoran, solver program for specified 2n-1, using faster algorithm than the brute-force approach

FORMULA

a(n) = A061808(n)/(2n-1).

EXAMPLE

For n = 11, 2n-1 = 21, 21*15 = 315 which has all odd digits.

For m = 1 to 14, n*m listed are 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, all of which contains at least one even digit.

MATHEMATICA

f[n_] := Block[{m = 1, nn = 2n -1, od = {1, 3, 5, 7, 9}}, While[ Union@ Join[od, IntegerDigits[m*nn]] != od, m += 2]; m]; Array[f, 75] (* Robert G. Wilson v, Dec 05 2017 *)

PROG

(PARI) isok(n, m) = {my(d = digits((2*n-1)*m)); #select(x->((x%2)==0), d) == 0; }

a(n) = {my(m=1); while (!isok(n, m), m++); m; } \\ Michel Marcus, Sep 24 2019

CROSSREFS

Cf. A061808, A216473.

Sequence in context: A279023 A272682 A111122 * A104436 A070601 A332843

Adjacent sequences:  A296006 A296007 A296008 * A296010 A296011 A296012

KEYWORD

base,nonn,look

AUTHOR

Yang Haoran, Dec 02 2017

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)